by means of the divergence of the axial-vector current. Here, \(m_{u(d)}\)  are the current-quark masses
of the pion's constituents. Following [1]}, [2]} we take the value \(2\,\,{\rm GeV}\)  for this parameter
at the initial scale \(\mu _0=2\,{\rm GeV}\) . Its uncertainty is, however, large Using, for instance, the values for the current-quark masses quoted in [3]}, one obtains
\(\mu _\pi (\mu _0)=2.64^{+0.11}_{-0.42}\,\,{\rm GeV}\)  for the case of the \(\pi ^0\) . Values
of \(1.8\,\,{\rm GeV}\)  and \(1.9\,\,{\rm GeV}\)  at \(\mu _0\)  are advocated for in [4]} and
[5]}, respectively..
The mass parameter evolves with the scale, see App. A.
For the factorization and renormalization scale we choose
\(\mu ^2_R\,=\,\mu ^2_F\,=\,\frac{\hat{t}\hat{u}}{\hat{s}}\) 
